MAT-098 Objectives


Course Description

This course is designed as a substitute for MAT-097 (Foundations of Algebra) for non-STEM students who will be taking MAT-181 (Statistics) for their program requirements. Topics include being able to summarize and analyze data distributions both numerically and graphically. Evaluating linear equations while understanding the concepts of slope, intercepts, inequalities, correlation and regression will be discussed. The concept of probability and probability distributions will be introduced for both discrete and continuous variables. A grade of C or higher in this course satisfies the prerequisite to MAT 171, MAT 172, MAT 173, and MAT 181. This course does not satisfy degree requirements. Prerequisite: Grade of C or better in Foundations of Mathematics (MAT093) or placement.

Learning Outcomes

  1. Summarize data numerically and graphically including bar charts, dot plots, histograms and box plots.
  2. Compare and analyze distributions both graphically and numerically
  3. Apply the concepts of mean, median and variability of quantitative data
  4. Analyze bivariate data and understand concepts of correlation and simple linear regression
  5. Evaluate linear equations, understand concepts of slope, intercepts, and inequalities
  6. Apply basic probability rules and be able to construct/analyze two-way tables
  7. Distinguish between discrete and continuous variables and their probability distributions
  8. Apply the concept of the Normal distribution and applicable techniques at a basic level.

Instructional Objectives

Distributions for Quantitative Data

  1. Develop a way to describe and distinguish graphs of a quantitative variable.
  2. Identify reasonable explanations for what might explain the differences seen in different data sets.
  3. Distinguish between categorical and quantitative variables.
  4. Identify graphs that represent the distribution of a quantitative variable.
  5. Analyze the distribution of a quantitative variable using a dot plot. Describe the shape, give a general estimate of center, and determine the overall range.
  6. Analyze the distribution of a quantitative variable using a histogram. Describe shape, give a general estimate of center and the overall range, and calculate relevant percentages.

Measures of Center

  1. Find the mean and median from different representations of data.
  2. Develop number sense with mean and median by creating different data sets with a given mean or median.

Quantifying and Measuring Variability Relative to the Median

  1. Use quartiles to quantify variability relative to the median.
  2. Create and interpret boxplots, relate boxplots to histograms and dotplots.
  3. Develop a strategy for measuring deviation from the mean.
  4. Use the concept of average deviation from the mean to estimate standard deviation from the mean.
  5. Estimate and calculate the standard deviation from the mean

Relationships in Categorical Data

  1. Use a two-way table to analyze the association between two categorical variables.

Introduction to Scatterplots and Association

  1. Read and interpret scatterplots
  2. Describe the pattern in a scatterplot as positive or negative association, if appropriate.
  3. Identify explanatory and response variables.
  4. Identify direction, strength and form in scatterplots.
  5. User to describe strength and direction for a linear relationship.

Introduction to Linear Regression 

  1. For a linear relationship, use the least squares regression line to summarize the overall pattern and to make predictions.
  2. Identify the rate of change and initial value for predicted values in a least squares regression line.
  3. Interpret the rate of change (slope) and initial value (y-intercept) for regression lines.

Types of Statistical Studies and Producing Data

  1. Distinguish between questions about a population and questions about cause and effect.
  2. Determine if a study is an experiment or an observational study.
  3. Explain how the study design impacts the types of conclusions.
  4. Define statistical bias.
  5. Identify situations in which samples may have voluntary response bias.
  6. Explain how random selection eliminates bias.
  7. Identify sampling plans that will tend to give the most accurate samples.
  8. Distinguish observational studies from experiments.
  9. Identify explanatory, response, and potential confounding variables in an experiment